Generalizations of Tucker–Fan–Shashkin Lemmas

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• 作者：Oleg R. Musin
• 关键词：Tucker lemma ; Ky Fan lemma ; Shashkin lemma ; Borsuk–Ulam theorem ; Degree of mapping
• 刊名：Arnold Mathematical Journal
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：2
• 期：3
• 页码：299-308
• 全文大小：457 KB
• 刊物类别：Mathematics, general; Algebraic Geometry; Mathematical Physics; Analysis; Dynamical Systems and Ergo
• 刊物主题：Mathematics, general; Algebraic Geometry; Mathematical Physics; Analysis; Dynamical Systems and Ergodic Theory; Combinatorics;
• 出版者：Springer International Publishing
• ISSN：2199-6806
• 卷排序：2

文摘

Tucker and Ky Fan’s lemma are combinatorial analogs of the Borsuk–Ulam theorem (BUT). In 1996, Yu. A. Shashkin proved a version of Fan’s lemma, which is a combinatorial analog of the odd mapping theorem (OMT). We consider generalizations of these lemmas for BUT–manifolds, i.e. for manifolds that satisfy BUT. Proofs rely on a generalization of the OMT and on a lemma about the doubling of manifolds with boundaries that are BUT–manifolds.